When playing pickup games in a park, gym, or other public space, it is customary to ask whether the game will happen within a "half court" or "full court". Half court games are common because they allow two games to fit on the same full court at once.
3-on-3 pickup games are usually played on half court, while 5-on-5 games are usually on a full court. This gives more room for a 3-on-3 game to operate without tiring people out, while 5-on-5 matchups almost always need a full court to operate smoothly.
Overall, the phrase full court may refer to a court or a pickup game that uses a full court. Both uses are well-known by frequent players of the game.
Finally, the term "full court" is also associated with the full court press, a defensive tactic teams use to try and force turnovers in the backcourt. You can read more about the full court press in Basketball Full Court Press.